Self-supervised diffusion model fine-tuning for costate initialization using Markov chain Monte Carlo

2025-10-02

AI Summary

Trajectory optimization for low-thrust spacecraft in multi-body environments suffers from poor initial guesses for costate variables and low global search efficiency. Method: This paper proposes a self-supervised fine-tuning framework integrating conditional diffusion models with Markov Chain Monte Carlo (MCMC). It employs a joint reward function combining constraint violation and objective value, enables efficient sampling via Metropolis random walks, and dynamically refines the generative distribution through reward-weighted training—requiring no external data. Contribution/Results: The method innovatively supports automatic Pareto-front completion and cross-task transfer. Evaluated on an Europa–Titan orbital transfer mission, it significantly improves solution-set density and quality over conventional standalone global search methods, effectively mitigating the sensitivity of indirect methods to initial costate guesses.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Global search and optimization of long-duration, low-thrust spacecraft trajectories with the indirect method is challenging due to a complex solution space and the difficulty of generating good initial guesses for the costate variables. This is particularly true in multibody environments. Given data that reveals a partial Pareto optimal front, it is desirable to find a flexible manner in which the Pareto front can be completed and fronts for related trajectory problems can be found. In this work we use conditional diffusion models to represent the distribution of candidate optimal trajectory solutions. We then introduce into this framework the novel approach of using Markov Chain Monte Carlo algorithms with self-supervised fine-tuning to achieve the aforementioned goals. Specifically, a random walk Metropolis algorithm is employed to propose new data that can be used to fine-tune the diffusion model using a reward-weighted training based on efficient evaluations of constraint violations and missions objective functions. The framework removes the need for separate focused and often tedious data generation phases. Numerical experiments are presented for two problems demonstrating the ability to improve sample quality and explicitly target Pareto optimality based on the theory of Markov chains. The first problem does so for a transfer in the Jupiter-Europa circular restricted three-body problem, where the MCMC approach completes a partial Pareto front. The second problem demonstrates how a dense and superior Pareto front can be generated by the MCMC self-supervised fine-tuning method for a Saturn-Titan transfer starting from the Jupiter-Europa case versus a separate dedicated global search.

Problem

• Optimizing low-thrust spacecraft trajectories in complex multibody environments
• Generating accurate initial guesses for costate variables indirectly
• Completing and discovering Pareto optimal fronts using existing data

Innovation

• Conditional diffusion models represent optimal trajectory solution distributions
• Markov Chain Monte Carlo with self-supervised fine-tuning generates new data
• Reward-weighted training optimizes constraint violations and mission objectives